We argue that field trajectories, which lead to cosmic acceleration and feature rapid
turns near the boundary of the moduli space, are in the Swampland. We obtain this result by
assuming the validity of the Swampland Distance Conjecture (SDC) in the presence of a positive
scalar potential and by focusing on hyperbolic spaces, as prototype geometries of infinite
distance limits of Calabi-Yau compactifications. We find that, in a quasi-de Sitter space with
Hubble rate H and acceleration parameter ϵ, the turning rate Ω is upper bounded
such as Ω/H < 𝒪(√(ϵ)). Therefore, field trajectories consistent with the
SDC can only have a negligible deviation from geodesics. This has direct implications for the
realization and consistency of multi-field scenarios in string theory. Moreover, it implies a
tension between asymptotic accelerating expansion, consistent with observations, and the de Sitter
conjecture.